Meta-analysis is the synthesis of findings from research projects, which enables an estimate of the average or pooled effect across various studies. This study presents findings from the intention to treat analysis for a series of educational evaluations in England using a two-stage meta-analysis with standardised outcome data and individual participant data meta-analyses. The research estimates the overall impact of educational trials on pupils eligible for Free School Meals (FSM) and the attainment gap in literacy and mathematics performance between FSM and non-FSM pupils based on analysis of 88 trials and data from over half a million pupils. For the meta-analyses, frequentist and Bayesian multilevel models were used to estimate the individual and pooled effect size across categories of explanatory variables such as age groups (key stages in England) and aspects of the type of interventions (one-to-one, small group, whole class). Results indicated that the overall impact of interventions on the literacy outcomes of FSM pupils was positive, with a pooled effect size of 0.06 (0.03, 0.08). However, for mathematics, no overall effect on FSM pupils was observed. Analysis of the attainment gap indicated that literacy outcomes for FSM pupils were improved by interventions marginally more than for non-FSM pupils (pooled attainment gap 0.01 (−0.01, 0.04)). The risk of bias assessment showed that estimates were consistent across different methodological approaches. Overall, evidence from this study can be used to identify, test and scale educational interventions in schools to improve educational outcomes for disadvantaged pupils.

中文翻译：

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教育干预对有资格获得免费校餐的学生影响的个人参与者数据元分析

荟萃分析是对研究项目结果的综合，它可以估计各种研究的平均或综合效应。本研究使用标准化结果数据和个体参与者数据荟萃分析的两阶段荟萃分析，展示了对英格兰一系列教育评估的意向分析的结果。该研究根据对超过 50 万名学生的 88 项试验和数据的分析，估计了教育试验对有资格获得免费校餐 (FSM) 的学生的总体影响，以及 FSM 和非 FSM 学生在读写能力和数学成绩方面的差距。对于荟萃分析，常客和贝叶斯多层次模型用于估计解释变量类别的个体和综合效应大小，例如年龄组（英格兰的关键阶段）和干预类型的各个方面（一对一、小组、全班） . 结果表明，干预措施对 FSM 学生识字结果的总体影响是积极的，合并效应大小为 0.06（0.03，0.08）。然而，对于数学，没有观察到对 FSM 学生的总体影响。对成绩差距的分析表明，干预措施对 FSM 学生的读写成绩的改善程度略高于非 FSM 学生（综合成绩差距 0.01（-0.01，0.04））。偏倚风险评估表明，不同方法学方法的估计值是一致的。全面的，